Windows 32bit workstations work on Windows 64bit server?

Will workstation that have 32bit software work with a server with a 64bit O/S?
The workstations are all 32-bit ranging from WinXP, Vista, Win7.
The server is Server 2003 32-bit.

I would like to install a 64-bit Windows O/S on the server.
Would the 32-bit workstations have a hard time with a 64bit server?
What would the disadvantages be if this is possible?

Reason is, I would like to keep costs down by upgrading the memory of my server from 4GB to 8+GB and realize that a 32-bit O/S on the server can not take advantage of the additional memory, hence the upgrade to a 64bit server.
I would like to upgrade the workstations to 64bit at a later date due to financial constraints.

Well I would think it would be like any other server out there, all they do is communicate with each other, you can have a linux server communicate with a windows operating system, but it all depends on what your doing.

But since your workstations have their own OS and do not rely on sever to provide an OS to work in you should be fine to have a 64 bit server OS working with a 32 bit workstation, you are going to have a faster server, keep in mind everything still has to run 32 bit applications in the server side for the workstations but you will see a increase of performance.

64-bit or 32-bit just determines what programs can be executed locally. If you are just running a file server, the files are just files and will be handled appropriately by the local software on the workstations, and served by the local OS on the server.

If you are running active applications (where you are connecting to the server's app space), most 64-bit applications have a 32-bit mode for workstations, but it's not the server OS but the application itself that you would need to examine.